Standard accounts of semantics for counterfactuals confront the true–true problem: when the antecedent and consequent of a counterfactual are both actually true, the counterfactual is automatically true. This problem presents a challenge to safety-based accounts of knowledge. In this paper, drawing on work by Angelika Kratzer, Alan Penczek, and Duncan Pritchard, we propose a revised understanding of semantics for counterfactuals utilizing machinery from generalized quantifier theory which enables safety theorists to meet the challenge of the true–true problem.
Penelope Maddy advances a purportedly naturalistic account of mathematical methodology which might be taken to answer the question 'What justifies axioms of set theory?' I argue that her account fails both to adequately answer this question and to be naturalistic. Further, the way in which it fails to answer the question deprives it of an analog to one of the chief attractions of naturalism. Naturalism is attractive to naturalists and nonnaturalists alike because it explains the reliability of scientific practice. Maddy's (...) account, on the other hand, appears to be unable to similarly explain the reliability of mathematical practice without violating one of its central tenets. (shrink)
In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered.
C. S. Jenkins has recently proposed an account of arithmetical knowledge designed to be realist, empiricist, and apriorist: realist in that what’s the case in arithmetic doesn’t rely on us being any particular way; empiricist in that arithmetic knowledge crucially depends on the senses; and apriorist in that it accommodates the time-honored judgment that there is something special about arithmetical knowledge, something we have historically labeled with ‘a priori’. I’m here concerned with the prospects for extending Jenkins’s account beyond arithmetic—in (...) particular, to set theory. After setting out the central elements of Jenkins’s account and entertaining challenges to extending it to set theory, I conclude that a satisfactory such extension is unlikely. (shrink)
Philip Kitcher's account of scientific progress incorporates a conception of explanatory unification that invites the so-called 'obsessive unifier' worry, to wit, that in our drive to unify the phenomena we might impose artificial structure on the world and consequently produce an incorrect view of how things, in fact, are. I argue that Kitcher's attempt to address this worry is unsatisfactory because it relies on an ability to choose between rival patterns of explanation which itself rests on the relevant choice having (...) already been made. I also suggest a way of answering the worry that Kitcher is not likely to endorse. (shrink)
This paper argues that Philip Kitcher's epistemology of mathematics, codified in his Naturalistic Constructivism, is not naturalistic on Kitcher's own conception of naturalism. Kitcher's conception of naturalism is committed to (i) explaining the correctness of belief-regulating norms and (ii) a realist notion of truth. Naturalistic Constructivism is unable to simultaneously meet both of these commitments.
Duncan Pritchard has argued that his basis-relative anti-luck construal of a safety condition on knowing avoids the problem with necessary truths that safety conditions are often thought to have, viz., that beliefs the contents of which are necessarily true are trivially safe. He has further argued that adding an ability condition to truth, belief, and his anti-luck safety conditions yields an adequate account of knowledge. In this paper, we argue that not only does Pritchard’s anti-luck safety condition have a problem (...) with necessary truths, adding an ability condition is of no help. Indeed, the same sort of case that precipitates Pritchard’s introduction of an ability condition shows the inadequacy of his completed anti-luck account of knowledge. Moreover, reconstruing safety as an anti-risk condition as Pritchard has recently done does not fix the problem we’ve identified. We conclude by entertaining a radical suggestion to the effect that the failures of safety-based accounts of modal knowledge are due to failures of doxastic success rather than failures to satisfy an anti-luck (or anti-risk) condition. Accepting this radical suggestion makes available the view that there is, after all, no special problem between safety and necessary truths. (shrink)
According to an influential contextualist solution to skepticism advanced by Keith DeRose, denials of skeptical hypotheses are, in most contexts, strong yet insensitive. The strength of such denials allows for knowledge of them, thus undermining skepticism, while the insensitivity of such denials explains our intuition that we do not know them. In this paper we argue that, under some well-motivated conditions, a negated skeptical hypothesis is strong only if it is sensitive. We also consider how a natural response on behalf (...) of DeRose appears to be equally available to his primary rival (viz., the sensitivity theorist). (shrink)
Philip Kitcher has advanced an epistemology of science that purports to be naturalistic. For Kitcher, this entails that his epistemology of science must explain the correctness of belief-regulating norms while endorsing a realist notion of truth. This paper concerns whether or not Kitcher's epistemology of science is naturalistic on these terms. I find that it is not but that by supplementing the account we can secure its naturalistic standing.
Philip Kitcher has argued against the apriority of mathematical knowledge in a number of places. His arguments rely on a conception of mathematical knowledge as embedded in a historical tradition and the claim that this sort of embedding compromises apriority. In this paper, I argue that tradition dependence of mathematical knowledge does not compromise its apriority. I further identify the factors which appear to lead Kitcher to argue as he does.
In this chapter, I consider some problems with naturalizing mathematics. More specifically, I consider how the two leading kinds of approach to naturalizing mathematics, to wit, Quinean indispensability‐based approaches and Maddy's Second Philosophical approach, seem to run afoul of constraints that any satisfactory naturalistic mathematics must meet. I then suggest that the failure of these kinds of approach to meet the relevant constraints indicates a general problem with naturalistic mathematics meeting these constraints, and thus with the project of naturalizing mathematics (...) itself. (shrink)